Iterative multiscale dynamic time warping (IMs-DTW): a tool for rainfall time series comparison

Abstract

In many domains, such as weather forecasting, hydrology or civil protection, it is an important issue to characterize rainfall variability and intermittency in, either or both, a given time period or area. A variety of sensors, for instance, rain gauges, weather radars, and satellites are widely used for this purpose. Techniques to establish the similarity between rainfall time series are commonly based on the comparison of some extracted characteristic parameters (cumulative rainfall height, extreme values, rain occurrence, mean rain rate, etc.). The present study focuses on the development of a tool allowing to compare directly rainfall time series at a fine temporal scale. It allows quantifying the dissimilarity between the time series and determining a non-linear relationship between their time axes. This study presents an algorithm based on a Multiscale Dynamic Time Warping (MsDTW) approach, it is based on the DTW algorithm applied on an iterative multiscale framework we called IMs-DTW. This proposed algorithm is well suited for rain time series allowing point-to-point pairing between pairs of rainfall time. It takes the intermittency and the non-stationarity of the precipitation process into account. An application to measurements observed by four pluviometers located in the Paris area makes it possible to interpret the obtained results and to compare the IMs-DTW with more usual statistical features.

From data to interpretable models: machine learning for soil moisture forecasting

“…There was, however, notable ground surface change resulting from surface erosion and sediment transport in response to each successive rain storm. To isolate the non-stationary behavior of ground surface conditions over time [ 13 ], we partitioned the data into four time periods, see Fig. 16 , bracketing rainfall from storms and related increases and subsequent decreases in soil moisture.…”

“…We studied raw soil moisture ( ) and rainfall measurements ( ) at one post-fire field setting and one controlled experimental setting. We did not evaluate the temporal variability, non-stationary behavior, or entropy of rainfall at the fine scale [ 13 , 44 ] in the context of post-fire erosion. Rainfall, though, is a multi-scale event with non-stationary temporal behavior that is outside the scope of this work.…”

“…In the case of irregular (or intermittent) observations [ 13 ], is processed to predict a soil moisture value via a model g : where has been compute recursively from previous data, previous estimates, and initial observation to .…”

Spatial and Time Warping for Gauge Adjustment of Rainfall Estimates

“…As mentioned in the Introduction, time or spatial warping methods have been applied on rainfall data in previous works, but not for position and timing correction. For example, dynamic time warping has been used to classify rainfall time series or to measure dissimilarities between them [8][9][10][11][12]. Spatial warping or similar methods have been used for position correction in the framework of data assimilation into numerical weather models.…”

“…Reference [10] used it in the framework of rainfall estimate validation, while the goal of [9] was to derive precipitation estimates from cloud top temperature. Reference [11] developed a multiscale DTW and used it as a dissimilarity measure. They applied it to yearly time series in Paris to study the impact of climate change on rainfall variability [12].…”